Optical waveguide having optimal index profile for multicomponent nonlinear glass

Abstract

A gradient index optical waveguide has an optimal index profile even though the relationship between concentration and refractive index is not linear. This is accomplished by varying the concentrations of the dopants as a function of the radial distance from the center of said core substantially as: C.sub.i (r)=C.sub.i.sup.0 +[(1-ξ.sub.i)(r/a).sup.α +ξ.sub.i (r/a) 2 α ]C i 1 where C i (r) denotes the concentration of the i th dopant as a function of radial distance r, C i 0 denotes the concentration at r=o of the i th dopant, C i 1 is the total change in concentration of dopants between r=o and r=a, α is the selected index profile, and ξ i are variable parameters relating the concentration of the i th dopant to radial distance r.

What is claimed is: 
     
       1. A gradient index optical waveguide comprising: a core having a radius a formed from silicate compounds with at least two dopants;   the refractive index of said core being n 1  at the radius r=0 and n 2  at the radius r=a, the concentrations of each compound being a function of the radial distance from the center of the core substantially as:   C.sub.i (r)=C.sub.i.sup.° +[(1-ξ.sub.i)(r/a).sup.α +ξ.sub.i (r/a).sup.2α ]C.sub.i.sup.1,     where C i  (r) denotes the concentration of the i th  dopant as a function of radial distance, C i .sup.° denotes the concentration at r=0 of the i th  dopant, C i   1  denotes the difference in concentration of the i th  dopant between r=a and r=o, α is the selected index profile, ξ i  are variable parameters relating the concentration of the i th  dopant to radial distance r, said parameters minimizing the factor δ(λ) by which the index of refraction profile differs from the profile produced where there is a linear relationship between index of refraction and said concentrations.     
     
     
       2. The optical waveguide recited in claim 1 wherein said variable parameters ξ i  are such that δ(λ) is zero, where δ(λ) is:   [+ΣP.sub.i C.sub.i.sup.1 ξ.sub.i +ΣP.sub.ij C.sub.i.sup.1 C.sub.j.sup.1 ]=0,     where P ij  are proportionality factors dependent upon the wavelength of the light with which said waveguide is used and i and j designate dopants.   
     
     
       3. The waveguide recited in claim 2 wherein said variable parameters ξ i  are such that the derivatives with respect to said wavelength of δ(λ) are zero, i.e.: ##EQU11## where λ s  is the wavelength of said light and k is less than or equal to the number of dopants present in the core. 
     
     
       4. The optical waveguide recited in claim 1 wherein said optical waveguide has a radial index of refraction n(r) given by: ##EQU12## and where δ(λ) is equal to zero. 
     
     
       5. An optical waveguide having a gradient index profile formed from multicomponent glasses of a specified composition comprising: a core formed from silicate compounds with at least two dopants:   the concentrations of said compounds in said core producing said specified composition; and   the concentrations of said compounds in said core being varied in relation to parameters which relate the concentration of the dopants to radial distance from the center of the core in accordance with:   C.sub.i (r)=C.sub.i.sup.° +[(1-ξ.sub.i)(r/a).sup.α +ξ.sub.i (r/a).sup.2α ]C.sub.i.sup.1,     where C i  (r) denotes the concentration of the i th  dopant as a function of radial distance, C i   o  denotes the concentration at r=0 of the i th  dopant, C i   1  denotes the difference in concentration of the i th  dopant between r=a and r=o, α is the selected index profile, and wherein ξ i  are variable parameters relating the concentration of i th  dopant to radial distance r, said parameters minimizing the factor δ(λ) by which the index of refraction profile differs from the profile produced where there is a linear relationship between index of refraction and said concentrations.